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Properties and Application of the Location‐Test V (n, k)
Author(s) -
Rey G.
Publication year - 1979
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710210307
Subject(s) - mathematics , quantile , statistics , statistic , test statistic , sample size determination , location parameter , normal distribution , f test of equality of variances , robustness (evolution) , generalization , z test , sample (material) , distribution (mathematics) , statistical hypothesis testing , combinatorics , probability distribution , mathematical analysis , biochemistry , chemistry , chromatography , gene
The present paper is concerned with the properties of a test statistic V ( n, k ) to test location differences in the one‐sample case with known hypothetical distribution G ( x ). The test is similar to the W ILCOXON two‐sample statistic after replacement of the second sample by quantiles of the hypothetical distribution. A comparison with the exact distribution of V ( n, k ) shows that an approximation by means of the normal distribution provides good results even for small sample sizes. The V ‐test is unbiased against one‐tailed alternatives and it is consistent with a restriction which is hardly relevant in practical applications. With regard to the application we are interested especially in the power and robustness against extreme observations for small sample size n . It is shown that in a normal distribution with known standard deviation V ( n, k ) is more powerful than S TUDENT's t for small n and more robust in the sense considered here. The test statistic is based on grouping of the observations into classes of equal expected frequency. A generalization to arbitrary classes provides an essential extension of applicability such as to discrete distributions and to situations where only relative frequencies of G ( x ) in fixed classes are known.